grammar - "Since" + Present Perfect

According to a grammar book (Advanced English Grammar in Use, Cambridge) we should use "since" as follows:

"We use the present perfect in the time clause with since if the two situations described in the main clause and the time clause extend until the present."
E.g. Since I´ve been able to drive, I've felt much more independent.

I wonder, is it correct to use simple present instead of present perfect in that sense? I.e, "Since I am able to drive."

Answer

They are both grammatically correct, but they have different meanings. The relevant ones here are:

7.
continuously from or counting from the time when:
He has been busy since he came.

8.
because; inasmuch as:
Since you're already here, you might as well stay.

Your first example has meaning #7

Since I´ve been able to drive, I've felt much more independent.

From the time I started driving until now, I have felt more independent.

But changing the tense changes the meaning to #8

Since I am able to drive, I feel more independent.

Because I can now drive, I feel more independent than I did before.